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49-521: The gulf and its major port of Cattigara had supposedly been reached by a 1st-century Greek trader named Alexander, who returned safely and left a periplus of his voyage. His account that Cattigara was "some days" sail from Zaba was taken by Marinus of Tyre to mean "numberless" days and by Ptolemy to mean "a few". Both Alexander and Marinus's works have been lost, but were claimed as authorities by Ptolemy in his Geography . Ptolemy (and presumably Marinus before him) followed Hipparchus in making

98-588: A belfry in Dunkerque and Montjuïc castle in Barcelona to estimate the length of the meridian arc through Dunkerque. The length of the first prototype metre bar was based on these measurements, but it was later determined that its length was short by about 0.2 millimetres because of miscalculation of the flattening of the Earth, making the prototype about 0.02% shorter than the original proposed definition of

147-480: A nautical mile as 6,080 feet, the length of one minute of arc at 48 degrees latitude. In 1793, France defined the metre so as to make the polar circumference of the Earth 40,000 kilometres. In order to measure this distance accurately, the French Academy of Sciences commissioned Jean Baptiste Joseph Delambre and Pierre Méchain to lead an expedition to attempt to accurately measure the distance between

196-700: A new form of the Dragon's Tail peninsula , including details from Marco Polo . As early as 1540, continuing exploration led Sebastian Münster to conflate the Great Gulf with the Pacific Ocean west of the Americas , supposing that the 1st-century Alexander had crossed to a port in Peru and safely returned. The idea was repeated by Ortelius and others. (Some modern South American scholars have returned to

245-460: Is a number that can be divided by all natural numbers from 1 to 10: some historians believe that Eratosthenes changed from the 250,000 value written by Cleomedes to this new value to simplify calculations; other historians of science, on the other side, believe that Eratosthenes introduced a new length unit based on the length of the meridian, as stated by Pliny, who writes about the stadion "according to Eratosthenes' ratio". Posidonius calculated

294-404: Is plagued by calculation errors and false assumptions. In 2012, Anthony Abreu Mora repeated Eratosthenes's calculation with more accurate data; the result was 40,074 km, which is 66 km different (0.16%) from the currently accepted polar circumference. Eratosthenes' method was actually more complicated, as stated by the same Cleomedes, whose purpose was to present a simplified version of

343-416: Is the distance around Earth . Measured around the equator , it is 40,075.017 km (24,901.461 mi). Measured passing through the poles , the circumference is 40,007.863 km (24,859.734 mi). Measurement of Earth's circumference has been important to navigation since ancient times. The first known scientific measurement and calculation was done by Eratosthenes , by comparing altitudes of

392-400: Is the most famous among the results obtained by Eratosthenes , who estimated that the meridian has a length of 252,000 stadia , with an error on the real value between −2.4% and +0.8% (assuming a value for the stadion between 155 and 160 metres; the exact value of the stadion remains a subject of debate to this day; see stadion ). Eratosthenes described his technique in a book entitled On

441-517: Is the name of a major port city located on the Magnus Sinus described by various antiquity sources. Modern scholars have linked Cattigara to the archaeological site of Óc Eo in present-day Vietnam . Cattigara was the name given by the 2nd-century Alexandrian geographer Claudius Ptolemy to the land on the easternmost shore of the Indian Sea at (due to a scribal error) 8½° south of

490-705: The Equator . The name "Cattigara" was probably derived from the Sanskrit Kirti-nagara कीर्ति- नगर "Renowned City" or Kotti-nagara कोटि-नगर "Strong City". Scholarship has determined that Ptolemy's Cattigara was at 8½° north of the Equator and was the forerunner of Saigon as the main port and entrepot at the mouth of the Mekong . On some medieval maps, for example on the Martellus map of 1489 or

539-508: The Gulf of Thailand , with Cattigara located in the Funanese Óc Eo ruins at Thoại Sơn . Its Cottiaris River would then be a former course of the Mekong which once passed the site to enter the Gulf of Thailand . Others ignoring the route as garbled but taking Cattigara to be the major Han entrepôt of Longbian consider the Great Gulf to have been the Gulf of Tonkin , hypothesizing that

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588-599: The Indian Ocean a landlocked sea, placing Cattigara on its unknown eastern shoreline . The expanse formed between it and the Malay Peninsula (the " Golden Chersonese "), he called the Great Gulf. Ptolemy's Geography was translated into Arabic by a team of scholars including al-Khwārizmī in the 9th century during the reign of al-Maʿmūn . By that time, Arab merchants such as Soleiman had begun regular commerce with Tang China and, having passed through

637-643: The Pacific Ocean west of South America , considered to represent a southeastern peninsula of Asia. Modern reconstructions agree in naming the Golden Chersonese a form of the Malay Peninsula but differ in their considerations of how much of the South China Sea to include within Ptolemy's reckoning of the Great Gulf. Those following Alexander's route from Zaba on its northern shore to Cattigara to its southeast consider it to be no more than

686-639: The Strait of Malacca en route , shown that the Indian Sea communicated with the open ocean . African traders similarly showed that the coastline did not turn sharply east south of Cape Prasum below Zanzibar as Ptolemy held. Al-Khwārizmī 's influential Book of the Description of the Earth , therefore, removed Ptolemy's unknown shores from the Indian Ocean. The robustly-described lands east of

735-402: The nautical mile in the seventeenth century and the metre in the eighteenth. Earth's polar circumference is very near to 21,600 nautical miles because the nautical mile was intended to express one minute of latitude (see meridian arc ), which is 21,600 partitions of the polar circumference (that is 60 minutes × 360 degrees). The polar circumference is also close to 40,000 kilometres because

784-589: The Antonines". Guided by Ptolemy, the discoverers of the New World were initially trying to find their way to Cattigara. On the 1489 map of the world made by Henricus Martellus Germanus , revising Ptolemy's work, Asia terminated in its southeastern point in a cape, the Cape of Cattigara. Writing of his 1499 voyage, Amerigo Vespucci said he had hoped to reach Malacca (Melaka) by sailing westward from Spain across

833-616: The Cape of Cattigara and sail through the strait separating Cattigara from the New World, into the Sinus Magnus to Malacca. This was the route he thought Marco Polo had gone from China to India in 1292. Columbus planned to meet up with the expedition sent at the same time from Portugal around the Cape of Good Hope under Vasco da Gama , and carried letters of credence from the Spanish monarchs to present to da Gama. On reaching Cariay on

882-633: The Earth in Ptolemaic Egypt . Using a vertical rod known as a gnomon and under the previous assumptions, he knew that at local noon on the summer solstice in Syene (modern Aswan , Egypt), the Sun was directly overhead, as the gnomon cast no shadow. Additionally, the shadow of someone looking down a deep well at that time in Syene blocked the reflection of the Sun on the water. Eratosthenes then measured

931-441: The Earth's circumference by reference to the position of the star Canopus . As explained by Cleomedes , Posidonius observed Canopus on but never above the horizon at Rhodes , while at Alexandria he saw it ascend as far as 7 + 1 ⁄ 2 degrees above the horizon (the meridian arc between the latitude of the two locales is actually 5 degrees 14 minutes). Since he thought Rhodes was 5,000 stadia due north of Alexandria, and

980-660: The Great Gulf, however, were retained as a phantom peninsula (now generally known as the Dragon's Tail ). Just after 1295, Maximus Planudes restored Ptolemy's Greek text and maps at Chora Monastery in Constantinople ( Istanbul ). This was translated into Latin at Florence by Jacobus Angelus around 1406 and quickly spread the work's information and misinformation throughout Western Europe. The maps initially repeated Ptolemy's enclosed Indian Sea. Following word of Bartholomew Dias 's circumnavigation of Africa, maps by Martellus and by Martin of Bohemia replaced this with

1029-657: The Gulf of Thailand (if present) was represented by the smaller inlet on the eastern shore of the Golden Chersonese. Its Cottiaris River would have been Vietnam 's Red River . Panyu ( Guangzhou ) had been the major port of the Kingdom of Nanyue but identifications of Ptolemy's Cattigara with Han-era Nanhai , though common in the past, are credited little more than those placing it in Peru. Cattigara Cattigara

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1078-683: The Roman Orient" added some weight to the conjecture that Óc Eo was the Ptolemaic Cattigara. The distinguished German classical scholar, Albrecht Dihle, supported this view, saying: From the account of the voyage of Alexander referred to by Ptolemy, Kattigara can actually be located only in the Mekong delta, because Alexander went first along the east coast of the Malacca peninsula, northward to Bangkok, from thence likewise only along

1127-469: The Sun's angle of elevation at noon in Alexandria by measuring the length of another gnomon's shadow on the ground. Using the length of the rod, and the length of the shadow, as the legs of a triangle, he calculated the angle of the sun's rays. This angle was about 7°, or 1/50th the circumference of a circle ; assuming the Earth to be perfectly spherical, he concluded that its circumference was 50 times

1176-687: The Waldseemüller map from 1507, published in the Ptolemy's Geography, Cattigara was located 8 and a half degrees below the equator and 178 degrees west of the Canary Islands. John Caverhill deduced in 1767 that Cattigara was the Mekong Delta port Banteaymeas (now Hà Tiên ), not far from Óc Eo. The plea in 1979 by Jeremy H.C.S. Davidson for "a thorough study of Hà-tiên in its historical context and in relation to Óc-eo" as indispensable for an accurate understanding and interpretation of

1225-589: The Western Ocean (the Atlantic ) around the Cape of Cattigara into the Sinus Magnus ("Great Gulf") that lay to the east of the Golden Chersonese ( Malay Peninsula ), of which the Cape of Cattigara formed the southeastern point. The Sinus Magnus was the actual Gulf of Thailand . Christopher Columbus , on his fourth and last voyage of 1502–1503, planned to follow the coast of Ciamba southward around

1274-590: The actual circumference of 24,901 mi (40,074 km). Strabo noted that the distance between Rhodes and Alexandria is 3,750 stadia, and reported Posidonius's estimate of the Earth's circumference to be 180,000 stadia or 18,000 mi (29,000 km). Pliny the Elder mentions Posidonius among his sources and—without naming him—reported his method for estimating the Earth's circumference. He noted, however, that Hipparchus had added some 26,000 stadia to Eratosthenes's estimate. The smaller value offered by Strabo and

1323-425: The basis for a unit of measurement for distance and proposed the nautical mile as one minute or one-sixtieth ( ⁠ 1 / 60 ⁠ ) of one degree of latitude. As one degree is ⁠ 1 / 360 ⁠ of a circle, one minute of arc is ⁠ 1 / 21600 ⁠ of a circle – such that the polar circumference of the Earth would be exactly 21,600 miles. Gunter used Snellius's circumference to define

1372-542: The circumnavigation of the world by the expedition led by Ferdinand Magellan that the Pacific Ocean was the Sinus Magnus and located Cattigara on the west coast of South America. In this he was followed by Oronce Fine and the makers of the Dieppe Maps but eventually geographers and cartographers had to admit that Cattigara could not be found. The mathematician and cosmographer Gemma Frisius said in 1531: "in

1421-453: The coast of Costa Rica , Columbus thought he was close to the gold mines of Ciamba. On 7 July 1503, he wrote from Jamaica : "I reached the land of Cariay...Here I received news of the gold mines of Ciamba which I was seeking". It was eventually realized that Columbus had not reached Ciamba or any part of the Cape of Cattigara. The search for Cattigara continued during the early years of the sixteenth century. Johannes Schöner concluded after

1470-526: The coast toward the south east, and so came to Kattigara. We hear nothing of any further change of course. In addition, at Óc Eo, an emporium excavated in the western Mekong delta, in the ancient kingdom of Fu-nan, Roman finds from the 2nd century after Christ have come to light. Adhir Chakravarti concluded: "The archaeological remains unearthed at Oc-Eo to the south of Phnom Bà Thên in the Trans-Bassac region of Cochin-China have proved beyond doubt that it

1519-459: The diameter of earth to be of 1,050 yojanas . The length of the yojana intended by Aryabhata is in dispute. One careful reading gives an equivalent of 14,200 kilometres (8,800 mi), too large by 11%. Another gives 15,360 km (9,540 mi), too large by 20%. Yet another gives 13,440 km (8,350 mi), too large by 5%. Around AD 830, Caliph Al-Ma'mun commissioned a group of Muslim astronomers led by Al-Khwarizmi to measure

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1568-433: The difference in the star's elevation indicated the distance between the two locales was 1/48 of the circle, he multiplied 5,000 by 48 to arrive at a figure of 240,000 stadia for the circumference of the earth. It is generally thought that the stadion used by Posidonius was almost exactly 1/10 of a modern statute mile. Thus Posidonius's measure of 240,000 stadia translates to 24,000 mi (39,000 km), not much short of

1617-527: The different lengths of Greek and Roman stadia have created a persistent confusion around Posidonius's result. Ptolemy used Posidonius's lower value of 180,000 stades (about 33% too low) for the earth's circumference in his Geography . This was the number used by Christopher Columbus in order to underestimate the distance to India as 70,000 stades. Around AD 525, the Indian mathematician and astronomer Aryabhata wrote Aryabhatiya , in which he calculated

1666-460: The distance from Tadmur ( Palmyra ) to Raqqa , in modern Syria . They calculated the Earth's circumference to be within 15% of the modern value, and possibly much closer. How accurate it actually was is not known because of uncertainty in the conversion between the medieval Arabic units and modern units, but in any case, technical limitations of the methods and tools would not permit an accuracy better than about 5%. A more convenient way to estimate

1715-468: The idea as recently as the 1990s, but there remains no substantial evidence to support the idea.) The Great Gulf was finally dispensed with in all its forms as more accurate accounts returned from both the East and West Indies . The details of the Great Gulf changed somewhat among its various forms, but the ancient and Renaissance Ptolemaic accounts had it bound on the west by the Golden Chersonese and on

1764-509: The known distance from Alexandria to Syene (5,000 stadia, a figure that was checked yearly), i.e. 250,000 stadia . Depending on whether he used the "Olympic stade" (176.4 m) or the Italian stade (184.8 m), this would imply a circumference of 44,100 km (an error of 10%) or 46,100 km, an error of 15%. A value for the stadion of 157.7 metres has even been posited by L.V. Firsov, which would give an even better precision, but

1813-540: The measure of the Earth , which has not been preserved; what has been preserved is the simplified version described by Cleomedes to popularise the discovery. Cleomedes invites his reader to consider two Egyptian cities, Alexandria and Syene (modern Aswan ): According to Cleomedes ' On the Circular Motions of the Celestial Bodies , around 240 BC, Eratosthenes calculated the circumference of

1862-461: The metre was originally defined to be one ten millionth (i.e., a kilometre is one ten thousandth) of the arc from pole to equator ( quarter meridian ). The accuracy of measuring the circumference has improved since then, but the physical length of each unit of measure had remained close to what it was determined to be at the time, so the Earth's circumference is no longer a round number in metres or nautical miles. The measure of Earth's circumference

1911-417: The mid-day sun at two places a known north–south distance apart. He achieved a great degree of precision in his computation. Treating the Earth as a sphere , its circumference would be its single most important measurement. Earth deviates from spherical by about 0.3%, as characterized by flattening . In modern times, Earth's circumference has been used to define fundamental units of measurement of length:

1960-478: The mouth of the Mekong. The "father of Early Southeast Asian history", George Coedès , has said: "By the middle of the 3rd century Fu-nan had already established relations with China and India, and it is doubtless on the west coast of the Gulf of Siam that the furthest point reached by Hellenistic navigators is to be found, that is the harbour of Kattigara mentioned by Ptolemy". A.H. Christie said in 1979 that "the presence of objects, however few in number, from

2009-560: The north and east by the ports of the Sinae , chief among which was Cattigara . Medieval Islamic cartographers followed al-Khwārizmī in having a strait southeast of the gulf communicating with the Sea of Darkness . Believing the circumference of the Earth to follow Ptolemy's reduced figures or even smaller ones, cartographers during the early phases of the Age of Discovery expanded the Gulf to form

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2058-513: The one described in Eratosthenes' book. Pliny, for example, has quoted a value of 252,000 stadia. The method was based on several surveying trips conducted by professional bematists , whose job was to precisely measure the extent of the territory of Egypt for agricultural and taxation-related purposes. Furthermore, the fact that Eratosthenes' measure corresponds precisely to 252,000 stadia (according to Pliny) might be intentional, since it

2107-459: The place where Ptolemy described Cattigara as projecting far beyond the Equator, and others by quite dubious reasoning as adjoining the kingdoms of Var, Moabar and other places now, following repeated voyages on both this side and the other of the Equator, no continental land was found but an almost infinite number of islands". Circumference of the Earth Earth's circumference

2156-461: The place where he made landfall was not Asia , but rather a New World . In 1617 the Dutch scientist Willebrord Snellius assessed the circumference of the Earth at 24,630 Roman miles (24,024 statute miles). Around that time British mathematician Edmund Gunter improved navigational tools including a new quadrant to determine latitude at sea. He reasoned that the lines of latitude could be used as

2205-498: The site, still remains unanswered. The 18th-century French geographer, Jean-Baptiste Bourguignon d'Anville , located Cattigara at the mouth of the Mekong ( Cottiaris ) River, where it is shown on his map, Orbis Veteribus Notus (The World Known to the Ancients). The Swedish yachtsman and writer Björn Landström also concluded, from the sailing directions given by the ancient merchant and seafarer Alexander, that Cattigara lay at

2254-404: The top of the mountain, he sighted the dip angle which, along with the mountain's height (which he determined beforehand), he applied to the law of sines formula. This was the earliest known use of dip angle and the earliest practical use of the law of sines. However, the method could not provide more accurate results than previous methods, due to technical limitations, and so al-Biruni accepted

2303-408: The value calculated the previous century by the al-Ma'mun expedition. 1,700 years after Eratosthenes's death, Christopher Columbus studied what Eratosthenes had written about the size of the Earth. Nevertheless, based on a map by Toscanelli , he chose to believe that the Earth's circumference was 25% smaller. If, instead, Columbus had accepted Eratosthenes's larger value, he would have known that

2352-477: Was a great port of Fou-nan and, as suggested by Mallaret and Coedès may be identified with Ptolemy's Kattigara emporium (= Skt Kirtinagara or Kottanagara )". The eminent scholar of ancient Indian civilization, Luciano Petech, concluded: "Kattigara was situated on the Mekong delta… At Go Oc Eo in western Cochinchina, along with Indian jewelry and Chinese bronze mirrors, several Roman objects were excavated: beads, gems, cammei, and, last but not least, Roman coins of

2401-463: Was provided in Al-Biruni 's Codex Masudicus (1037). In contrast to his predecessors, who measured the Earth's circumference by sighting the Sun simultaneously from two locations, al-Biruni developed a new method of using trigonometric calculations, based on the angle between a plain and mountain top, which made it possible for it to be measured by a single person from a single location. From

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